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The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.

\"3D Character Development Workshop is designed to fast-track comprehension of the concepts, tools, and methods of character rigging so that you can get past the technical hurdles and on to animating. This comprehensive guide is simple enough for non-technical artists to follow, yet presented in a holistic, comprehensive, best-practices approach so professional and student animators and artists can begin designing and animating their own fully-functioning characters\" -- Amazon.com.

This book provides new and seasoned users with step-by-step procedures on creating and modifying 3D models, working with cameras and lights, assigning materials to objects, rendering, and printing. Unlike many AutoCAD competitors, it uses both metric and imperial units to illustrate the myriad tools for this popular application. Use the companion CD to set up drawing exercises and projects and see all of the book's figures including color. This book includes 50 \"mini-workshops,\" that complete small projects from concept through actual plotting. Solving all of the workshops will simulate the creation of full projects (architectural and mechanical) from beginning to end, without overlooking any of the basic commands and functions in AutoCAD 2017.

We live in a 3-D world, but most three-dimensional objects are designed from a series of two-dimensional side elevations and plan views. This book will teach you how to think and design in the third dimension. Through 60 construction projects, you will learn how folded paper units can be joined to create beautiful 3-D structures, according to the principles of three-dimensional symmetry. In addition to over 80 specially commissioned photographs and 300 step-by-step illustrations, this accessible book contains QR codes or hyperlinks to 30 short videos that show a selection of the projects rotating through 360 degrees.

This book provides new and seasoned users with step-by-step procedures on creating and modifying 3D models, working with cameras and lights, assigning materials to objects, rendering, and printing. Unlike many AutoCAD competitors, it uses both metric and imperial units to illustrate the myriad tools for this popular application. Use the companion files to set up drawing exercises and projects and see all of the book's figures including color. This book includes 50 \"mini-workshops,\" that complete small projects from concept through actual plotting. Solving all of the workshops will simulate the creation of full projects (architectural and mechanical) from beginning to end, without overlooking any of the basic commands and functions in AutoCAD 2021.

\"Sketches are the foundations of great art, where thoughts and concepts first come to life as an image. The process is no different for a 3D artist. In Sketching from the Imagination in ZBrush, fifty talented digital artists showcase their ZBrush artwork, share their inspirations, and explain their approaches to sculpting in 3D. From rough models moulded in digital clay, to entire characters, creatures, animals and more, Sketching from the Imagination presents a stunning visual adventure into 3D sketching. Packed with useful tips and creative insights, this book is an invaluable resource that will inspire 3D artists of all abilities.\" -- Provided by publisher.

Discover how to build impressive 3D graphics with the next-generation graphics API—Vulkan About This Book • Get started with the Vulkan API and its programming techniques using the easy-to-follow examples to create stunning 3D graphics • Understand memory management in Vulkan and implement image and buffer resources • Get hands-on with the drawing process and synchronization, and render a 3D graphics scene with the Vulkan graphics pipeline Who This Book Is For This book is ideal for graphic programmers who want to get up and running with Vulkan. It's also great for programmers who have experience with OpenGL and other graphic APIs who want to take advantage of next generation APIs. A good knowledge of C/C++ is expected. What You Will Learn • Learn fundamentals of Vulkan programing model to harness the power of modern GPU devices. • Implement device, command buffer and queues to get connected with the physical hardware. • Explore various validation layers and learn how to use it for debugging Vulkan application. • Get a grip on memory management to control host and device memory operations. • Understand and implement buffer and image resource types in Vulkan. • Define drawing operations in the Render pass and implement graphics pipeline. • Manage GLSL shader using SPIR-V and update the shader resources with descriptor sets and push constants. • Learn the drawing process, manage resources with synchronization objects and render 3D scene output on screen with Swapchain. • Bring realism to your rendered 3D scene with textures, and implement linear and optimal textures In Detail Vulkan, the next generation graphics and compute API, is the latest offering by Khronos. This API is the successor of OpenGL and unlike OpenGL, it offers great flexibility and high performance capabilities to control modern GPU devices. With this book, you'll get great insights into the workings of Vulkan and how you can make stunning graphics run with minimum hardware requirements. We begin with a brief introduction to the Vulkan system and show you its distinct features with the successor to the OpenGL API. First, you will see how to establish a connection with hardware devices to query the available queues, memory types, and capabilities offered. Vulkan is verbose, so before diving deep into programing, you'll get to grips with debugging techniques so even first-timers can overcome error traps using Vulkan's layer and extension features. You'll get a grip on command buffers and acquire the knowledge to record various operation commands into command buffer and submit it to a proper queue for GPU processing. We'll take a detailed look at memory management and demonstrate the use of buffer and image resources to create drawing textures and image views for the presentation engine and vertex buffers to store geometry information. You'll get a brief overview of SPIR-V, the new way to manage shaders, and you'll define the drawing operations as a single unit of work in the Render pass with the help of attachments and subpasses. You'll also create frame buffers and build a solid graphics pipeline, as well as making use of the synchronizing mechanism to manage GPU and CPU hand-shaking. By the end, you'll know everything you need to know to get your hands dirty with the coolest Graphics API on the block. Style and approach This book takes a practical approach to guide you through the Vulkan API, and you will get to build an application throughout the course of the book. Since you are expected to be familiar with C/C++, there is not much hand-holding throughout the course of the book.